Unfortunately, some of the pumps sold as pond pumps don't really function well in a "water garden" type pond. As you have discovered, the strainers get clogged very easily with fish and plant "stuff" I think having the pump in a "cage" will help but eventually you will have clogging problems there as well. I think suspending the pump off the bottom will help as it won't draw as much stuff off the floor to clog the strainer. I'm concerned that removing part of the strainer may let something get into the impeller and cause it to malfuntion. Could you set the pump into a cage that has larger openings that the pump strainer but small enough to catch stuff so you wouldn't have to clean the pump as often? I would also set the cage on something to elevate it off the floor. I have see some comments where people have put their pump into a cage with furnace filter material all around it to keep stuff off the pump strainer.

My pump has a cage with holes. It finally clogs yearly or so. The holes are probably a quarter inch or so. It is big enough to let some crud through. Sometimes the pump gets a tangle in the impeller and sometimes the cage clogs first. It is probably a good size compromise. I would think some hardware cloth wrapped around could do the trick.

I adapted a well pump filter to attach to the input to the impeller as the pre-filter. It has worked well for over 10 years despite some unusual challenges like the very small gravel in a pre-planted pot dropped in the pond by the raccoons. (The pot landed upside down on top of the pre-filter and the gravel got sucked right in. I don't buy from that nursery any more.They also used potting soil with perlite and styrofoam beads.) Regular pump maintenance takes care of most other problems.

I really don't care for sponge pre-filters. Without almost constant attention they clog and put far too much strain on the motor. I use a pump and pre-filter that can deal with all but the larger debris that gets removed with a net anyway, while the water with finer particulates goes through the pump into the Skippy where it is filtered quite nicely by quilt batting.Once while spring cleaning, the pump was running without the pre-filter on the intake and a fish tried to swim into the intake and got stuck. It was not easy to remove him.

Get 2 of the "water lily" baskets they sell at home depot. The ones with all the little holes that are useless for waterlilies. Cut a hole just big enough for the cord and the tubing to go thru in the side of one. Attach the pump and zip tie the 2 baskets together. I've been using these for years on all my pumps (I did find bigger 12" ones to use for the 4200gph pump). The little stuff gets pumped thru to the filter and they don't clog.
Mine lay any-which-way in the pond but you can stand them up and put a pot on top if you want.
Sherry

I keep my pump in a large plastic flower pot with a furnace filter closing the top which acts as the prefilter. I have some rocks to weight the pot down. I have a nylon cord through a cork (drill a hole through the center of the cork) which is attached to the lip of the pot that I use to hook the pot to pull it out of the water about once a month to rinse the prefilter.